## The area of a rectangle is represented by the function x3 − 2×2 − 40x − 64. The width of the rectangle is x + 4. Find the expression represe

Question

The area of a rectangle is represented by the function x3 − 2×2 − 40x − 64. The width of the rectangle is x + 4. Find the expression representing the length of the rectangle.

A. x2 − 8x − 20

B. x2 + 12x + 20

C. x2 − 6x − 16

D. x2 + 10x + 16

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2021-09-11T17:14:51+00:00
2021-09-11T17:14:51+00:00 1 Answer
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## Answers ( )

Answer:Step-by-step explanation:If the area is

and area = length * width and our width is given as x + 4, then the length is found by dividing the area by the width. You could do that using long division, but it’s easier using synthetic division.

-4 | 1 -2 -40 -64

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1

This is how you start. The -4 inside the box comes from the factor you are dividing by. If x + 4 = 0, then x = -4. The numbers after are the coefficients from each descending power of x. Multiply the -4 by the 1 and put that product up under the -2 and add to get:

-4 | 1 -2 -40 -64

-4

——————————–

1 -6

Now multiply -4 by -6 and put that product up under the -40 and add:

-4 | 1 -2 -40 -64

-4 24

————————-

1 -6 -16

Multiplying -4 by -16 gives you 64 so when you add you get a remainder of 0.

The numbers under the line give you the depressed polynomial

That gives you the expression for the length. That’s C.